Mass data storage devices have always been essential to computer technology. The disk drive is one familiar mass storage device. Although the surface of the disk is two-dimensional, the data is stored in one-dimensional tracks on the disk. This results in a one-dimensional data stream, or bit stream, as shown in FIG. 1a. Data bits, indexed as n-2, n-1, n, n+1, n+2, etc., are arranged in successive positions on the track. This is a one-dimensional array, which may either be represented linearly, as shown in FIG. 1a (rectangular coordinates), or may be understood as being arranged around the perimeter of a circular track (polar coordinates). In either case, the bits are arranged one-dimensionally. (Note that that the legend "n Dimension" in FIG. 1a refers not to n distinct dimensions, but rather to the single dimension, along whose length the bits, indexed as stated, are deployed.)
Each bit in the data stream is adjacent to only two bits, its immediate neighbors in the positive and negative directions in one dimension. As recording density increases, high frequency components in the recorded signal increase. Due to bandwidth limitations, those increased high frequency components may not be faithfully reproduced. This causes "smearing" of the data bits. This smearing manifests itself as interaction and distortion between adjacent bits in the data stream. In a one-dimensional data stream, such interaction and distortion can only occur in one dimension.
There are also mass storage devices which utilize two-dimensional recording technology, such as holographic storage. The data in such a device is not stored in one-dimensional tracks, but rather is stored in the form of two dimensional arrays, as shown in FIG. 1b. Each bit is adjacent to as many as eight other bits, its immediate neighbors in the eight combinations of the positive and negative directions in two dimensions x and y, including diagonally adjacent bits. Interaction and distortion may occur between all adjacent bits in both dimensions.
One approach to dealing with data interaction and distortion is to encode the recorded data so as to reduce the high frequency components which must be reproduced. In essence, encoding the data low-pass filters the data before it is recorded. Although low-pass filtering encoding schemes have been developed for one-dimensional data streams, these schemes are not generally applicable to two-dimensional recording. In two-dimensional recording, the high frequency components must be reduced in both dimensions.